LMFDB - Embedded newform 29.14.b.a.28.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,14,Mod(28,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 14, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.28");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	29.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$31.0969693961$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			28.12
Character	$\chi$	$=$	29.28
Dual form			29.14.b.a.28.21

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-53.0296i q^{2} +485.442i q^{3} +5379.86 q^{4} +48264.8 q^{5} +25742.8 q^{6} -490607. q^{7} -719711. i q^{8} +1.35867e6 q^{9} +O(q^{10})$	\(q-53.0296i q^{2} +485.442i q^{3} +5379.86 q^{4} +48264.8 q^{5} +25742.8 q^{6} -490607. q^{7} -719711. i q^{8} +1.35867e6 q^{9} -2.55946e6i q^{10} -9.51508e6i q^{11} +2.61161e6i q^{12} -5.59430e6 q^{13} +2.60167e7i q^{14} +2.34298e7i q^{15} +5.90584e6 q^{16} +1.65225e8i q^{17} -7.20497e7i q^{18} -2.82460e8i q^{19} +2.59658e8 q^{20} -2.38161e8i q^{21} -5.04581e8 q^{22} +1.00862e9 q^{23} +3.49378e8 q^{24} +1.10879e9 q^{25} +2.96664e8i q^{26} +1.43351e9i q^{27} -2.63940e9 q^{28} +(-4.92131e8 - 3.16519e9i) q^{29} +1.24247e9 q^{30} -3.21172e9i q^{31} -6.20905e9i q^{32} +4.61902e9 q^{33} +8.76181e9 q^{34} -2.36790e10 q^{35} +7.30945e9 q^{36} -1.18798e10i q^{37} -1.49788e10 q^{38} -2.71571e9i q^{39} -3.47367e10i q^{40} +1.54576e10i q^{41} -1.26296e10 q^{42} -2.42476e10i q^{43} -5.11898e10i q^{44} +6.55758e10 q^{45} -5.34865e10i q^{46} +1.33465e10i q^{47} +2.86695e9i q^{48} +1.43806e11 q^{49} -5.87984e10i q^{50} -8.02071e10 q^{51} -3.00966e10 q^{52} -9.77753e10 q^{53} +7.60183e10 q^{54} -4.59243e11i q^{55} +3.53095e11i q^{56} +1.37118e11 q^{57} +(-1.67849e11 + 2.60975e10i) q^{58} +5.94235e11 q^{59} +1.26049e11i q^{60} +8.06015e10i q^{61} -1.70316e11 q^{62} -6.66572e11 q^{63} -2.80883e11 q^{64} -2.70008e11 q^{65} -2.44945e11i q^{66} +6.25714e11 q^{67} +8.88887e11i q^{68} +4.89624e11i q^{69} +1.25569e12i q^{70} -3.99505e11 q^{71} -9.77848e11i q^{72} -8.98089e11i q^{73} -6.29980e11 q^{74} +5.38251e11i q^{75} -1.51960e12i q^{76} +4.66816e12i q^{77} -1.44013e11 q^{78} -3.07669e11i q^{79} +2.85044e11 q^{80} +1.47027e12 q^{81} +8.19710e11 q^{82} -1.10824e12 q^{83} -1.28127e12i q^{84} +7.97454e12i q^{85} -1.28584e12 q^{86} +(1.53652e12 - 2.38901e11i) q^{87} -6.84810e12 q^{88} +2.99029e12i q^{89} -3.47746e12i q^{90} +2.74460e12 q^{91} +5.42621e12 q^{92} +1.55911e12 q^{93} +7.07758e11 q^{94} -1.36329e13i q^{95} +3.01414e12 q^{96} +3.31755e12i q^{97} -7.62598e12i q^{98} -1.29278e13i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 131436 q^{4} - 90794 q^{5} - 191952 q^{6} + 398260 q^{7} - 18624674 q^{9}+O(q^{10}) $ 32 * q - 131436 * q^4 - 90794 * q^5 - 191952 * q^6 + 398260 * q^7 - 18624674 * q^9	\( 32 q - 131436 q^{4} - 90794 q^{5} - 191952 q^{6} + 398260 q^{7} - 18624674 q^{9} + 5240482 q^{13} + 549733588 q^{16} + 593107012 q^{20} - 1351453384 q^{22} + 1866943772 q^{23} + 4550583596 q^{24} + 7169723618 q^{25} - 13976463456 q^{28} - 10157197956 q^{29} + 21508715952 q^{30} - 8142086534 q^{33} + 21000232616 q^{34} - 15057663628 q^{35} + 116060443480 q^{36} - 86572746688 q^{38} + 13537077480 q^{42} + 263177965664 q^{45} + 513778986120 q^{49} - 372662169044 q^{51} - 101448215388 q^{52} + 573910354530 q^{53} + 1479431015408 q^{54} + 500871600416 q^{57} - 969686686880 q^{58} + 1024205768724 q^{59} + 1751113369840 q^{62} - 4168751771256 q^{63} - 2804312517964 q^{64} - 781490399506 q^{65} - 872679676184 q^{67} - 1363415929136 q^{71} - 6756459308672 q^{74} - 23715100786248 q^{78} + 1267893681036 q^{80} + 25379587936536 q^{81} + 4236061808312 q^{82} + 6421393088172 q^{83} - 16601603597496 q^{86} + 3240260232764 q^{87} + 3526967972716 q^{88} - 5472886962916 q^{91} + 1684734140256 q^{92} + 3555997675886 q^{93} + 29362958775032 q^{94} - 39622013504436 q^{96}+O(q^{100}) \) 32 * q - 131436 * q^4 - 90794 * q^5 - 191952 * q^6 + 398260 * q^7 - 18624674 * q^9 + 5240482 * q^13 + 549733588 * q^16 + 593107012 * q^20 - 1351453384 * q^22 + 1866943772 * q^23 + 4550583596 * q^24 + 7169723618 * q^25 - 13976463456 * q^28 - 10157197956 * q^29 + 21508715952 * q^30 - 8142086534 * q^33 + 21000232616 * q^34 - 15057663628 * q^35 + 116060443480 * q^36 - 86572746688 * q^38 + 13537077480 * q^42 + 263177965664 * q^45 + 513778986120 * q^49 - 372662169044 * q^51 - 101448215388 * q^52 + 573910354530 * q^53 + 1479431015408 * q^54 + 500871600416 * q^57 - 969686686880 * q^58 + 1024205768724 * q^59 + 1751113369840 * q^62 - 4168751771256 * q^63 - 2804312517964 * q^64 - 781490399506 * q^65 - 872679676184 * q^67 - 1363415929136 * q^71 - 6756459308672 * q^74 - 23715100786248 * q^78 + 1267893681036 * q^80 + 25379587936536 * q^81 + 4236061808312 * q^82 + 6421393088172 * q^83 - 16601603597496 * q^86 + 3240260232764 * q^87 + 3526967972716 * q^88 - 5472886962916 * q^91 + 1684734140256 * q^92 + 3555997675886 * q^93 + 29362958775032 * q^94 - 39622013504436 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	53.0296i		−	0.585900i	−0.956128	−	0.292950i	$-0.905363\pi$
$2$		−	53.0296i		−	0.585900i	0.956128	−	0.292950i	$-0.0946370\pi$
$3$			485.442i			0.384459i	0.981350	+	0.192229i	$0.0615717\pi$
$3$			485.442i			0.384459i	−0.981350	+	0.192229i	$0.938428\pi$
$4$	5379.86			0.656721
$5$	48264.8			1.38142			0.690709	−	0.723133i	$-0.257298\pi$
$5$	48264.8			1.38142			0.690709	+	0.723133i	$0.257298\pi$
$6$	25742.8			0.225254
$7$	−490607.			−1.57615			−0.788073	−	0.615582i	$-0.788921\pi$
$7$	−490607.			−1.57615			−0.788073	+	0.615582i	$0.788921\pi$
$8$		−	719711.i		−	0.970673i
$9$	1.35867e6			0.852192
$10$		−	2.55946e6i		−	0.809373i
$11$		−	9.51508e6i		−	1.61942i	−0.586829	−	0.809711i	$-0.699624\pi$
$11$		−	9.51508e6i		−	1.61942i	0.586829	−	0.809711i	$-0.300376\pi$
$12$			2.61161e6i			0.252482i
$13$	−5.59430e6			−0.321451			−0.160725	−	0.986999i	$-0.551383\pi$
$13$	−5.59430e6			−0.321451			−0.160725	+	0.986999i	$0.551383\pi$
$14$			2.60167e7i			0.923464i
$15$			2.34298e7i			0.531098i
$16$	5.90584e6			0.0880039
$17$			1.65225e8i			1.66019i	0.557623	+	0.830094i	$0.311713\pi$
$17$			1.65225e8i			1.66019i	−0.557623	+	0.830094i	$0.688287\pi$
$18$		−	7.20497e7i		−	0.499299i
$19$		−	2.82460e8i		−	1.37740i	−0.725048	−	0.688699i	$-0.758182\pi$
$19$		−	2.82460e8i		−	1.37740i	0.725048	−	0.688699i	$-0.241818\pi$
$20$	2.59658e8			0.907207
$21$		−	2.38161e8i		−	0.605963i
$22$	−5.04581e8			−0.948819
$23$	1.00862e9			1.42067			0.710337	−	0.703862i	$-0.248542\pi$
$23$	1.00862e9			1.42067			0.710337	+	0.703862i	$0.248542\pi$
$24$	3.49378e8			0.373183
$25$	1.10879e9			0.908317
$26$			2.96664e8i			0.188338i
$27$			1.43351e9i			0.712091i
$28$	−2.63940e9			−1.03509
$29$	−4.92131e8	−	3.16519e9i	−0.153636	−	0.988127i
$29$	−4.92131e8	−	3.16519e9i	−0.153636	−	0.988127i
$30$	1.24247e9			0.311170
$31$		−	3.21172e9i		−	0.649960i	−0.945721	−	0.324980i	$-0.894642\pi$
$31$		−	3.21172e9i		−	0.649960i	0.945721	−	0.324980i	$-0.105358\pi$
$32$		−	6.20905e9i		−	1.02223i
$33$	4.61902e9			0.622601
$34$	8.76181e9			0.972705
$35$	−2.36790e10			−2.17732
$36$	7.30945e9			0.559652
$37$		−	1.18798e10i		−	0.761197i	−0.924740	−	0.380598i	$-0.875718\pi$
$37$		−	1.18798e10i		−	0.761197i	0.924740	−	0.380598i	$-0.124282\pi$
$38$	−1.49788e10			−0.807017
$39$		−	2.71571e9i		−	0.123584i
$40$		−	3.47367e10i		−	1.34091i
$41$			1.54576e10i			0.508214i	0.967176	+	0.254107i	$0.0817816\pi$
$41$			1.54576e10i			0.508214i	−0.967176	+	0.254107i	$0.918218\pi$
$42$	−1.26296e10			−0.355034
$43$		−	2.42476e10i		−	0.584957i	−0.956272	−	0.292478i	$-0.905520\pi$
$43$		−	2.42476e10i		−	0.584957i	0.956272	−	0.292478i	$-0.0944799\pi$
$44$		−	5.11898e10i		−	1.06351i
$45$	6.55758e10			1.17723
$46$		−	5.34865e10i		−	0.832373i
$47$			1.33465e10i			0.180605i	0.995914	+	0.0903027i	$0.0287834\pi$
$47$			1.33465e10i			0.180605i	−0.995914	+	0.0903027i	$0.971217\pi$
$48$			2.86695e9i			0.0338338i
$49$	1.43806e11			1.48424
$50$		−	5.87984e10i		−	0.532183i
$51$	−8.02071e10			−0.638274
$52$	−3.00966e10			−0.211103
$53$	−9.77753e10			−0.605949			−0.302974	−	0.952999i	$-0.597980\pi$
$53$	−9.77753e10			−0.605949			−0.302974	+	0.952999i	$0.597980\pi$
$54$	7.60183e10			0.417214
$55$		−	4.59243e11i		−	2.23710i
$56$			3.53095e11i			1.52992i
$57$	1.37118e11			0.529552
$58$	−1.67849e11	+	2.60975e10i	−0.578944	+	0.0900154i
$59$	5.94235e11			1.83409			0.917043	−	0.398787i	$-0.130569\pi$
$59$	5.94235e11			1.83409			0.917043	+	0.398787i	$0.130569\pi$
$60$			1.26049e11i			0.348783i
$61$			8.06015e10i			0.200308i	0.994972	+	0.100154i	$0.0319336\pi$
$61$			8.06015e10i			0.200308i	−0.994972	+	0.100154i	$0.968066\pi$
$62$	−1.70316e11			−0.380812
$63$	−6.66572e11			−1.34318
$64$	−2.80883e11			−0.510923
$65$	−2.70008e11			−0.444058
$66$		−	2.44945e11i		−	0.364782i
$67$	6.25714e11			0.845065			0.422532	−	0.906348i	$-0.361141\pi$
$67$	6.25714e11			0.845065			0.422532	+	0.906348i	$0.361141\pi$
$68$			8.88887e11i			1.09028i
$69$			4.89624e11i			0.546190i
$70$			1.25569e12i			1.27569i
$71$	−3.99505e11			−0.370120			−0.185060	−	0.982727i	$-0.559248\pi$
$71$	−3.99505e11			−0.370120			−0.185060	+	0.982727i	$0.559248\pi$
$72$		−	9.77848e11i		−	0.827199i
$73$		−	8.98089e11i		−	0.694578i	−0.937758	−	0.347289i	$-0.887102\pi$
$73$		−	8.98089e11i		−	0.694578i	0.937758	−	0.347289i	$-0.112898\pi$
$74$	−6.29980e11			−0.445985
$75$			5.38251e11i			0.349210i
$76$		−	1.51960e12i		−	0.904566i
$77$			4.66816e12i			2.55245i
$78$	−1.44013e11			−0.0724081
$79$		−	3.07669e11i		−	0.142399i	−0.997462	−	0.0711997i	$-0.977317\pi$
$79$		−	3.07669e11i		−	0.142399i	0.997462	−	0.0711997i	$-0.0226828\pi$
$80$	2.85044e11			0.121570
$81$	1.47027e12			0.578422
$82$	8.19710e11			0.297763
$83$	−1.10824e12			−0.372071			−0.186036	−	0.982543i	$-0.559564\pi$
$83$	−1.10824e12			−0.372071			−0.186036	+	0.982543i	$0.559564\pi$
$84$		−	1.28127e12i		−	0.397949i
$85$			7.97454e12i			2.29342i
$86$	−1.28584e12			−0.342726
$87$	1.53652e12	−	2.38901e11i	0.379894	−	0.0590667i
$88$	−6.84810e12			−1.57193
$89$			2.99029e12i			0.637791i	0.947790	+	0.318895i	$0.103312\pi$
$89$			2.99029e12i			0.637791i	−0.947790	+	0.318895i	$0.896688\pi$
$90$		−	3.47746e12i		−	0.689741i
$91$	2.74460e12			0.506653
$92$	5.42621e12			0.932987
$93$	1.55911e12			0.249883
$94$	7.07758e11			0.105817
$95$		−	1.36329e13i		−	1.90276i
$96$	3.01414e12			0.393007
$97$			3.31755e12i			0.404391i	0.979345	+	0.202196i	$0.0648077\pi$
$97$			3.31755e12i			0.404391i	−0.979345	+	0.202196i	$0.935192\pi$
$98$		−	7.62598e12i		−	0.869614i
$99$		−	1.29278e13i		−	1.38006i
$100$	5.96511e12			0.596511
$101$		−	2.73310e12i		−	0.256193i	−0.991762	−	0.128096i	$-0.959113\pi$
$101$		−	2.73310e12i		−	0.256193i	0.991762	−	0.128096i	$-0.0408867\pi$
$102$			4.25335e12i			0.373965i
$103$	−1.24840e13			−1.03018			−0.515089	−	0.857137i	$-0.672241\pi$
$103$	−1.24840e13			−1.03018			−0.515089	+	0.857137i	$0.672241\pi$
$104$			4.02628e12i			0.312023i
$105$		−	1.14948e13i		−	0.837088i
$106$			5.18498e12i			0.355025i
$107$	9.12309e12			0.587689			0.293845	−	0.955853i	$-0.405065\pi$
$107$	9.12309e12			0.587689			0.293845	+	0.955853i	$0.405065\pi$
$108$			7.71207e12i			0.467645i
$109$	−9.63352e12			−0.550190			−0.275095	−	0.961417i	$-0.588709\pi$
$109$	−9.63352e12			−0.550190			−0.275095	+	0.961417i	$0.588709\pi$
$110$	−2.43535e13			−1.31072
$111$	5.76694e12			0.292648
$112$	−2.89745e12			−0.138707
$113$			3.30921e13i			1.49525i	0.664119	+	0.747627i	$0.268807\pi$
$113$			3.30921e13i			1.49525i	−0.664119	+	0.747627i	$0.731193\pi$
$114$		−	7.27133e12i		−	0.310265i
$115$	4.86806e13			1.96255
$116$	−2.64759e12	−	1.70283e13i	−0.100896	−	0.648924i
$117$	−7.60081e12			−0.273938
$118$		−	3.15120e13i		−	1.07459i
$119$		−	8.10605e13i		−	2.61670i
$120$	1.68626e13			0.515523
$121$	−5.60141e13			−1.62253
$122$	4.27426e12			0.117361
$123$	−7.50377e12			−0.195387
$124$		−	1.72786e13i		−	0.426843i
$125$	−5.40170e12			−0.126653
$126$			3.53481e13i			0.786968i
$127$			1.74752e13i			0.369571i	0.982779	+	0.184785i	$0.0591590\pi$
$127$			1.74752e13i			0.369571i	−0.982779	+	0.184785i	$0.940841\pi$
$128$		−	3.59694e13i		−	0.722884i
$129$	1.17708e13			0.224892
$130$			1.43184e13i			0.260173i
$131$			8.80284e13i			1.52181i	0.648865	+	0.760903i	$0.275244\pi$
$131$			8.80284e13i			1.52181i	−0.648865	+	0.760903i	$0.724756\pi$
$132$	2.48497e13			0.408875
$133$			1.38577e14i			2.17098i
$134$		−	3.31814e13i		−	0.495123i
$135$			6.91879e13i			0.983695i
$136$	1.18914e14			1.61150
$137$			5.04216e13i			0.651527i	0.945451	+	0.325764i	$0.105621\pi$
$137$			5.04216e13i			0.651527i	−0.945451	+	0.325764i	$0.894379\pi$
$138$	2.59646e13			0.320013
$139$	−9.89042e12			−0.116310			−0.0581552	−	0.998308i	$-0.518522\pi$
$139$	−9.89042e12			−0.116310			−0.0581552	+	0.998308i	$0.518522\pi$
$140$	−1.27390e14			−1.42989
$141$	−6.47894e12			−0.0694353
$142$			2.11856e13i			0.216853i
$143$			5.32303e13i			0.520564i
$144$	8.02408e12			0.0749962
$145$	−2.37526e13	−	1.52767e14i	−0.212236	−	1.36502i
$146$	−4.76253e13			−0.406953
$147$			6.98096e13i			0.570627i
$148$		−	6.39115e13i		−	0.499894i
$149$	2.34578e14			1.75621			0.878106	−	0.478467i	$-0.158807\pi$
$149$	2.34578e14			1.75621			0.878106	+	0.478467i	$0.158807\pi$
$150$	2.85433e13			0.204602
$151$	−2.00749e14			−1.37817			−0.689084	−	0.724681i	$-0.741987\pi$
$151$	−2.00749e14			−1.37817			−0.689084	+	0.724681i	$0.741987\pi$
$152$	−2.03290e14			−1.33700
$153$			2.24486e14i			1.41480i
$154$	2.47551e14			1.49548
$155$		−	1.55013e14i		−	0.897867i
$156$		−	1.46101e13i		−	0.0811605i
$157$			1.69756e14i			0.904644i	0.891855	+	0.452322i	$0.149404\pi$
$157$			1.69756e14i			0.904644i	−0.891855	+	0.452322i	$0.850596\pi$
$158$	−1.63156e13			−0.0834318
$159$		−	4.74643e13i		−	0.232962i
$160$		−	2.99679e14i		−	1.41213i
$161$	−4.94834e14			−2.23919
$162$		−	7.79679e13i		−	0.338898i
$163$			2.28376e14i			0.953741i	0.878974	+	0.476870i	$0.158229\pi$
$163$			2.28376e14i			0.953741i	−0.878974	+	0.476870i	$0.841771\pi$
$164$			8.31597e13i			0.333755i
$165$	2.22936e14			0.860072
$166$			5.87695e13i			0.217997i
$167$	3.46979e12			0.0123779			0.00618894	−	0.999981i	$-0.498030\pi$
$167$	3.46979e12			0.0123779			0.00618894	+	0.999981i	$0.498030\pi$
$168$	−1.71407e14			−0.588192
$169$	−2.71579e14			−0.896670
$170$	4.22887e14			1.34371
$171$		−	3.83770e14i		−	1.17381i
$172$		−	1.30449e14i		−	0.384153i
$173$	6.58203e14			1.86664			0.933319	−	0.359048i	$-0.116898\pi$
$173$	6.58203e14			1.86664			0.933319	+	0.359048i	$0.116898\pi$
$174$	−1.26688e13	−	8.14810e13i	−0.0346072	−	0.222580i
$175$	−5.43978e14			−1.43164
$176$		−	5.61946e13i		−	0.142515i
$177$			2.88467e14i			0.705130i
$178$	1.58574e14			0.373682
$179$	−3.05237e14			−0.693572			−0.346786	−	0.937944i	$-0.612727\pi$
$179$	−3.05237e14			−0.693572			−0.346786	+	0.937944i	$0.612727\pi$
$180$	3.52789e14			0.773114
$181$	1.11499e14			0.235701			0.117850	−	0.993031i	$-0.462400\pi$
$181$	1.11499e14			0.235701			0.117850	+	0.993031i	$0.462400\pi$
$182$		−	1.45545e14i		−	0.296848i
$183$	−3.91274e13			−0.0770102
$184$		−	7.25911e14i		−	1.37901i
$185$		−	5.73374e14i		−	1.05153i
$186$		−	8.26788e13i		−	0.146406i
$187$	1.57213e15			2.68855
$188$			7.18022e13i			0.118607i
$189$		−	7.03289e14i		−	1.12236i
$190$	−7.22947e14			−1.11483
$191$			6.45713e14i			0.962326i	0.876631	+	0.481163i	$0.159786\pi$
$191$			6.45713e14i			0.962326i	−0.876631	+	0.481163i	$0.840214\pi$
$192$		−	1.36353e14i		−	0.196429i
$193$		−	8.02507e12i		−	0.0111770i	−0.999984	−	0.00558851i	$-0.998221\pi$
$193$		−	8.02507e12i		−	0.0111770i	0.999984	−	0.00558851i	$-0.00177889\pi$
$194$	1.75929e14			0.236933
$195$		−	1.31073e14i		−	0.170722i
$196$	7.73657e14			0.974729
$197$	−1.25802e15			−1.53341			−0.766706	−	0.641999i	$-0.778105\pi$
$197$	−1.25802e15			−1.53341			−0.766706	+	0.641999i	$0.778105\pi$
$198$	−6.85559e14			−0.808576
$199$	2.58156e14			0.294671			0.147336	−	0.989087i	$-0.452930\pi$
$199$	2.58156e14			0.294671			0.147336	+	0.989087i	$0.452930\pi$
$200$		−	7.98004e14i		−	0.881678i
$201$			3.03748e14i			0.324892i
$202$	−1.44935e14			−0.150103
$203$	2.41443e14	+	1.55286e15i	0.242153	+	1.55743i
$204$	−4.31503e14			−0.419168
$205$			7.46057e14i			0.702057i
$206$			6.62022e14i			0.603581i
$207$	1.37037e15			1.21069
$208$	−3.30391e13			−0.0282889
$209$	−2.68763e15			−2.23059
$210$	−6.09565e14			−0.490450
$211$			1.81676e15i			1.41730i	0.705562	+	0.708648i	$0.250695\pi$
$211$			1.81676e15i			1.41730i	−0.705562	+	0.708648i	$0.749305\pi$
$212$	−5.26017e14			−0.397939
$213$		−	1.93937e14i		−	0.142296i
$214$		−	4.83794e14i		−	0.344327i
$215$		−	1.17030e15i		−	0.808070i
$216$	1.03171e15			0.691207
$217$			1.57569e15i			1.02443i
$218$			5.10862e14i			0.322356i
$219$	4.35971e14			0.267036
$220$		−	2.47066e15i		−	1.46915i
$221$		−	9.24318e14i		−	0.533669i
$222$		−	3.05819e14i		−	0.171463i
$223$	9.62729e14			0.524231			0.262115	−	0.965037i	$-0.415580\pi$
$223$	9.62729e14			0.524231			0.262115	+	0.965037i	$0.415580\pi$
$224$			3.04620e15i			1.61119i
$225$	1.50647e15			0.774060
$226$	1.75486e15			0.876070
$227$	−3.03390e15			−1.47175			−0.735874	−	0.677119i	$-0.763228\pi$
$227$	−3.03390e15			−1.47175			−0.735874	+	0.677119i	$0.763228\pi$
$228$	7.37677e14			0.347768
$229$			3.61654e15i			1.65715i	0.559876	+	0.828576i	$0.310849\pi$
$229$			3.61654e15i			1.65715i	−0.559876	+	0.828576i	$0.689151\pi$
$230$		−	2.58151e15i		−	1.14986i
$231$	−2.26612e15			−0.981309
$232$	−2.27802e15	+	3.54192e14i	−0.959149	+	0.149130i
$233$	−1.19435e15			−0.489009			−0.244505	−	0.969648i	$-0.578625\pi$
$233$	−1.19435e15			−0.489009			−0.244505	+	0.969648i	$0.578625\pi$
$234$			4.03068e14i			0.160500i
$235$			6.44165e14i			0.249492i
$236$	3.19690e15			1.20448
$237$	1.49356e14			0.0547467
$238$	−4.29861e15			−1.53312
$239$	4.08895e15			1.41914			0.709570	−	0.704635i	$-0.248889\pi$
$239$	4.08895e15			1.41914			0.709570	+	0.704635i	$0.248889\pi$
$240$			1.38372e14i			0.0467387i
$241$	3.57173e15			1.17427			0.587134	−	0.809489i	$-0.300256\pi$
$241$	3.57173e15			1.17427			0.587134	+	0.809489i	$0.300256\pi$
$242$			2.97040e15i			0.950639i
$243$			2.99921e15i			0.934470i
$244$			4.33625e14i			0.131547i
$245$	6.94077e15			2.05035
$246$			3.97922e14i			0.114477i
$247$			1.58017e15i			0.442765i
$248$	−2.31151e15			−0.630899
$249$		−	5.37986e14i		−	0.143046i
$250$			2.86450e14i			0.0742060i
$251$		−	7.19894e15i		−	1.81715i	−0.417727	−	0.908573i	$-0.637173\pi$
$251$		−	7.19894e15i		−	1.81715i	0.417727	−	0.908573i	$-0.362827\pi$
$252$	−3.58607e15			−0.882094
$253$		−	9.59705e15i		−	2.30067i
$254$	9.26703e14			0.216532
$255$	−3.87118e15			−0.881723
$256$	−4.20844e15			−0.934461
$257$	−8.58039e14			−0.185755			−0.0928777	−	0.995678i	$-0.529607\pi$
$257$	−8.58039e14			−0.185755			−0.0928777	+	0.995678i	$0.529607\pi$
$258$		−	6.24201e14i		−	0.131764i
$259$			5.82830e15i			1.19976i
$260$	−1.45260e15			−0.291622
$261$	−6.68643e14	−	4.30045e15i	−0.130927	−	0.842074i
$262$	4.66811e15			0.891627
$263$		−	8.27985e15i		−	1.54280i	−0.636349	−	0.771401i	$-0.719556\pi$
$263$		−	8.27985e15i		−	1.54280i	0.636349	−	0.771401i	$-0.280444\pi$
$264$		−	3.32436e15i		−	0.604342i
$265$	−4.71910e15			−0.837069
$266$	7.34869e15			1.27198
$267$	−1.45161e15			−0.245204
$268$	3.36626e15			0.554972
$269$		−	5.46598e15i		−	0.879586i	−0.898099	−	0.439793i	$-0.855052\pi$
$269$		−	5.46598e15i		−	0.879586i	0.898099	−	0.439793i	$-0.144948\pi$
$270$	3.66901e15			0.576347
$271$			8.49183e15i			1.30227i	0.758962	+	0.651135i	$0.225707\pi$
$271$			8.49183e15i			1.30227i	−0.758962	+	0.651135i	$0.774293\pi$
$272$			9.75792e14i			0.146103i
$273$			1.33235e15i			0.194787i
$274$	2.67384e15			0.381730
$275$		−	1.05502e16i		−	1.47095i
$276$			2.63411e15i			0.358695i
$277$	−5.92606e15			−0.788220			−0.394110	−	0.919063i	$-0.628947\pi$
$277$	−5.92606e15			−0.788220			−0.394110	+	0.919063i	$0.628947\pi$
$278$			5.24485e14i			0.0681462i
$279$		−	4.36367e15i		−	0.553891i
$280$			1.70420e16i			2.11346i
$281$	−5.62539e15			−0.681650			−0.340825	−	0.940127i	$-0.610706\pi$
$281$	−5.62539e15			−0.681650			−0.340825	+	0.940127i	$0.610706\pi$
$282$			3.43576e14i			0.0406821i
$283$	−2.73568e14			−0.0316558			−0.0158279	−	0.999875i	$-0.505038\pi$
$283$	−2.73568e14			−0.0316558			−0.0158279	+	0.999875i	$0.505038\pi$
$284$	−2.14928e15			−0.243066
$285$	6.61798e15			0.731533
$286$	2.82278e15			0.304999
$287$		−	7.58360e15i		−	0.801020i
$288$		−	8.43605e15i		−	0.871140i
$289$	−1.73947e16			−1.75623
$290$	−8.10119e15	+	1.25959e15i	−0.799764	+	0.124349i
$291$	−1.61048e15			−0.155472
$292$		−	4.83159e15i		−	0.456144i
$293$		−	9.03844e14i		−	0.0834553i	−0.999129	−	0.0417277i	$-0.986714\pi$
$293$		−	9.03844e14i		−	0.0834553i	0.999129	−	0.0417277i	$-0.0132862\pi$
$294$	3.70198e15			0.334330
$295$	2.86806e16			2.53364
$296$	−8.54999e15			−0.738873
$297$	1.36399e16			1.15318
$298$		−	1.24396e16i		−	1.02896i
$299$	−5.64250e15			−0.456677
$300$			2.89572e15i			0.229334i
$301$			1.18960e16i			0.921977i
$302$			1.06456e16i			0.807469i
$303$	1.32676e15			0.0984956
$304$		−	1.66817e15i		−	0.121216i
$305$			3.89021e15i			0.276710i
$306$	1.19044e16			0.828931
$307$			2.13842e16i			1.45779i	0.684627	+	0.728893i	$0.259965\pi$
$307$			2.13842e16i			1.45779i	−0.684627	+	0.728893i	$0.740035\pi$
$308$			2.51141e16i			1.67624i
$309$		−	6.06026e15i		−	0.396060i
$310$	−8.22028e15			−0.526060
$311$		−	5.40553e15i		−	0.338763i	−0.985551	−	0.169381i	$-0.945823\pi$
$311$		−	5.40553e15i		−	0.338763i	0.985551	−	0.169381i	$-0.0541770\pi$
$312$	−1.95453e15			−0.119960
$313$	3.17483e15			0.190846			0.0954229	−	0.995437i	$-0.469580\pi$
$313$	3.17483e15			0.190846			0.0954229	+	0.995437i	$0.469580\pi$
$314$	9.00210e15			0.530031
$315$	−3.21720e16			−1.85549
$316$		−	1.65522e15i		−	0.0935167i
$317$			1.53787e16i			0.851205i	0.904910	+	0.425602i	$0.139938\pi$
$317$			1.53787e16i			0.851205i	−0.904910	+	0.425602i	$0.860062\pi$
$318$	−2.51701e15			−0.136493
$319$	−3.01171e16	+	4.68266e15i	−1.60020	+	0.248802i
$320$	−1.35568e16			−0.705799
$321$			4.42874e15i			0.225942i
$322$			2.62408e16i			1.31194i
$323$	4.66695e16			2.28674
$324$	7.90986e15			0.379862
$325$	−6.20288e15			−0.291979
$326$	1.21107e16			0.558797
$327$		−	4.67652e15i		−	0.211525i
$328$	1.11250e16			0.493310
$329$		−	6.54787e15i		−	0.284660i
$330$		−	1.18222e16i		−	0.503916i
$331$		−	2.33871e16i		−	0.977452i	−0.872437	−	0.488726i	$-0.837462\pi$
$331$		−	2.33871e16i		−	0.977452i	0.872437	−	0.488726i	$-0.162538\pi$
$332$	−5.96217e15			−0.244347
$333$		−	1.61407e16i		−	0.648685i
$334$		−	1.84002e14i		−	0.00725221i
$335$	3.02000e16			1.16739
$336$		−	1.40654e15i		−	0.0533271i
$337$		−	2.78658e16i		−	1.03628i	−0.855296	−	0.518140i	$-0.826624\pi$
$337$		−	2.78658e16i		−	1.03628i	0.855296	−	0.518140i	$-0.173376\pi$
$338$			1.44017e16i			0.525359i
$339$	−1.60643e16			−0.574863
$340$			4.29019e16i			1.50613i
$341$	−3.05598e16			−1.05256
$342$	−2.03512e16			−0.687733
$343$	−2.30179e16			−0.763226
$344$	−1.74512e16			−0.567802
$345$			2.36316e16i			0.754517i
$346$		−	3.49043e16i		−	1.09366i
$347$	2.52401e16			0.776158			0.388079	−	0.921626i	$-0.373139\pi$
$347$	2.52401e16			0.776158			0.388079	+	0.921626i	$0.373139\pi$
$348$	8.26625e15	−	1.28525e15i	0.249484	−	0.0387904i
$349$	4.25101e16			1.25929			0.629646	−	0.776882i	$-0.283200\pi$
$349$	4.25101e16			1.25929			0.629646	+	0.776882i	$0.283200\pi$
$350$			2.88469e16i			0.838798i
$351$		−	8.01947e15i		−	0.228902i
$352$	−5.90796e16			−1.65543
$353$	1.96705e15			0.0541103			0.0270552	−	0.999634i	$-0.491387\pi$
$353$	1.96705e15			0.0541103			0.0270552	+	0.999634i	$0.491387\pi$
$354$	1.52973e16			0.413136
$355$	−1.92820e16			−0.511291
$356$			1.60873e16i			0.418851i
$357$	3.93502e16			1.00601
$358$			1.61866e16i			0.406364i
$359$		−	2.76316e16i		−	0.681227i	−0.940203	−	0.340614i	$-0.889365\pi$
$359$		−	2.76316e16i		−	0.681227i	0.940203	−	0.340614i	$-0.110635\pi$
$360$		−	4.71956e16i		−	1.14271i
$361$	−3.77309e16			−0.897224
$362$		−	5.91275e15i		−	0.138097i
$363$		−	2.71916e16i		−	0.623795i
$364$	1.47656e16			0.332730
$365$		−	4.33461e16i		−	0.959503i
$366$			2.07491e15i			0.0451203i
$367$		−	3.18933e16i		−	0.681350i	−0.940181	−	0.340675i	$-0.889344\pi$
$367$		−	3.18933e16i		−	0.681350i	0.940181	−	0.340675i	$-0.110656\pi$
$368$	5.95672e15			0.125025
$369$			2.10018e16i			0.433096i
$370$	−3.04058e16			−0.616092
$371$	4.79692e16			0.955064
$372$	8.38777e15			0.164103
$373$	5.86207e16			1.12705			0.563526	−	0.826099i	$-0.309445\pi$
$373$	5.86207e16			1.12705			0.563526	+	0.826099i	$0.309445\pi$
$374$		−	8.33693e16i		−	1.57522i
$375$		−	2.62221e15i		−	0.0486928i
$376$	9.60560e15			0.175309
$377$	2.75313e15	+	1.77070e16i	0.0493864	+	0.317634i
$378$	−3.72951e16			−0.657590
$379$		−	5.86072e16i		−	1.01577i	−0.861425	−	0.507886i	$-0.830427\pi$
$379$		−	5.86072e16i		−	1.01577i	0.861425	−	0.507886i	$-0.169573\pi$
$380$		−	7.33430e16i		−	1.24958i
$381$	−8.48320e15			−0.142085
$382$	3.42419e16			0.563827
$383$	1.54877e16			0.250724			0.125362	−	0.992111i	$-0.459991\pi$
$383$	1.54877e16			0.250724			0.125362	+	0.992111i	$0.459991\pi$
$384$	1.74611e16			0.277919
$385$			2.25308e17i			3.52599i
$386$	−4.25566e14			−0.00654862
$387$		−	3.29444e16i		−	0.498495i
$388$			1.78480e16i			0.265572i
$389$		−	9.04105e16i		−	1.32296i	−0.749963	−	0.661479i	$-0.769929\pi$
$389$		−	9.04105e16i		−	1.32296i	0.749963	−	0.661479i	$-0.230071\pi$
$390$	−6.95076e15			−0.100026
$391$			1.66648e17i			2.35859i
$392$		−	1.03499e17i		−	1.44071i
$393$	−4.27327e16			−0.585072
$394$			6.67126e16i			0.898426i
$395$		−	1.48496e16i		−	0.196713i
$396$		−	6.95500e16i		−	0.906313i
$397$	4.01455e15			0.0514634			0.0257317	−	0.999669i	$-0.491808\pi$
$397$	4.01455e15			0.0514634			0.0257317	+	0.999669i	$0.491808\pi$
$398$		−	1.36899e16i		−	0.172648i
$399$	−6.72712e16			−0.834652
$400$	6.54831e15			0.0799354
$401$	1.26735e17			1.52215			0.761076	−	0.648663i	$-0.224672\pi$
$401$	1.26735e17			1.52215			0.761076	+	0.648663i	$0.224672\pi$
$402$	1.61077e16			0.190354
$403$			1.79673e16i			0.208930i
$404$		−	1.47037e16i		−	0.168247i
$405$	7.09623e16			0.799043
$406$	8.23478e16	−	1.28036e16i	0.912500	−	0.141877i
$407$	−1.13037e17			−1.23270
$408$			5.77259e16i			0.619555i
$409$			1.48632e17i			1.57004i	0.619470	+	0.785020i	$0.287347\pi$
$409$			1.48632e17i			1.57004i	−0.619470	+	0.785020i	$0.712653\pi$
$410$	3.95631e16			0.411335
$411$	−2.44768e16			−0.250485
$412$	−6.71622e16			−0.676539
$413$	−2.91536e17			−2.89079
$414$		−	7.26704e16i		−	0.709341i
$415$	−5.34889e16			−0.513986
$416$			3.47353e16i			0.328598i
$417$		−	4.80123e15i		−	0.0447165i
$418$			1.42524e17i			1.30690i
$419$	2.17433e16			0.196306			0.0981530	−	0.995171i	$-0.468707\pi$
$419$	2.17433e16			0.196306			0.0981530	+	0.995171i	$0.468707\pi$
$420$		−	6.18404e16i		−	0.549733i
$421$		−	1.44748e16i		−	0.126701i	−0.997991	−	0.0633503i	$-0.979821\pi$
$421$		−	1.44748e16i		−	0.126701i	0.997991	−	0.0633503i	$-0.0201785\pi$
$422$	9.63419e16			0.830394
$423$			1.81334e16i			0.153910i
$424$			7.03699e16i			0.588178i
$425$			1.83199e17i			1.50798i
$426$	−1.02844e16			−0.0833711
$427$		−	3.95436e16i		−	0.315715i
$428$	4.90810e16			0.385948
$429$	−2.58402e16			−0.200135
$430$	−6.20608e16			−0.473448
$431$	9.83978e16			0.739406			0.369703	−	0.929150i	$-0.379459\pi$
$431$	9.83978e16			0.739406			0.369703	+	0.929150i	$0.379459\pi$
$432$			8.46607e15i			0.0626668i
$433$			8.04059e16i			0.586295i	0.956067	+	0.293148i	$0.0947027\pi$
$433$			8.04059e16i			0.586295i	−0.956067	+	0.293148i	$0.905297\pi$
$434$	8.35584e16			0.600215
$435$	7.41597e16	−	1.15305e16i	0.524793	−	0.0815959i
$436$	−5.18270e16			−0.361322
$437$		−	2.84894e17i		−	1.95683i
$438$		−	2.31193e16i		−	0.156457i
$439$	−2.61967e17			−1.74674			−0.873369	−	0.487058i	$-0.838070\pi$
$439$	−2.61967e17			−1.74674			−0.873369	+	0.487058i	$0.838070\pi$
$440$	−3.30522e17			−2.17149
$441$	1.95385e17			1.26485
$442$	−4.90162e16			−0.312676
$443$			4.40717e16i			0.277035i	0.990360	+	0.138518i	$0.0442338\pi$
$443$			4.40717e16i			0.277035i	−0.990360	+	0.138518i	$0.955766\pi$
$444$	3.10253e16			0.192188
$445$			1.44326e17i			0.881056i
$446$		−	5.10531e16i		−	0.307147i
$447$			1.13874e17i			0.675190i
$448$	1.37803e17			0.805290
$449$		−	2.23587e17i		−	1.28779i	−0.765113	−	0.643896i	$-0.777317\pi$
$449$		−	2.23587e17i		−	1.28779i	0.765113	−	0.643896i	$-0.222683\pi$
$450$		−	7.98876e16i		−	0.453522i
$451$	1.47080e17			0.823013
$452$			1.78031e17i			0.981965i
$453$		−	9.74519e16i		−	0.529849i
$454$			1.60887e17i			0.862297i
$455$	1.32468e17			0.699900
$456$		−	9.86855e16i		−	0.514022i
$457$	3.72137e16			0.191094			0.0955472	−	0.995425i	$-0.469540\pi$
$457$	3.72137e16			0.191094			0.0955472	+	0.995425i	$0.469540\pi$
$458$	1.91784e17			0.970926
$459$	−2.36851e17			−1.18221
$460$	2.61895e17			1.28885
$461$			2.49986e17i			1.21300i	0.795085	+	0.606498i	$0.207426\pi$
$461$			2.49986e17i			1.21300i	−0.795085	+	0.606498i	$0.792574\pi$
$462$			1.20172e17i			0.574949i
$463$	2.96941e17			1.40086			0.700428	−	0.713723i	$-0.252992\pi$
$463$	2.96941e17			1.40086			0.700428	+	0.713723i	$0.252992\pi$
$464$	−2.90645e15	−	1.86931e16i	−0.0135206	−	0.0869591i
$465$	7.52499e16			0.345193
$466$			6.33358e16i			0.286511i
$467$			2.63357e17i			1.17486i	0.809277	+	0.587428i	$0.199859\pi$
$467$			2.63357e17i			1.17486i	−0.809277	+	0.587428i	$0.800141\pi$
$468$	−4.08913e16			−0.179901
$469$	−3.06980e17			−1.33194
$470$	3.41598e16			0.146177
$471$	−8.24068e16			−0.347798
$472$		−	4.27677e17i		−	1.78030i
$473$	−2.30718e17			−0.947292
$474$		−	7.92028e15i		−	0.0320761i
$475$		−	3.13188e17i		−	1.25111i
$476$		−	4.36094e17i		−	1.71844i
$477$	−1.32844e17			−0.516384
$478$		−	2.16835e17i		−	0.831474i
$479$			3.05614e17i			1.15609i	0.816004	+	0.578046i	$0.196185\pi$
$479$			3.05614e17i			1.15609i	−0.816004	+	0.578046i	$0.803815\pi$
$480$	1.45477e17			0.542907
$481$			6.64590e16i			0.244687i
$482$		−	1.89407e17i		−	0.688004i
$483$		−	2.40213e17i		−	0.860876i
$484$	−3.01348e17			−1.06555
$485$			1.60121e17i			0.558633i
$486$	1.59047e17			0.547506
$487$	1.60477e16			0.0545100			0.0272550	−	0.999629i	$-0.491323\pi$
$487$	1.60477e16			0.0545100			0.0272550	+	0.999629i	$0.491323\pi$
$488$	5.80097e16			0.194434
$489$	−1.10863e17			−0.366674
$490$		−	3.68066e17i		−	1.20130i
$491$		−	3.16523e17i		−	1.01947i	−0.860331	−	0.509736i	$-0.829743\pi$
$491$		−	3.16523e17i		−	1.01947i	0.860331	−	0.509736i	$-0.170257\pi$
$492$	−4.03692e16			−0.128315
$493$	5.22968e17	−	8.13122e16i	1.64048	−	0.255065i
$494$	8.37958e16			0.259416
$495$		−	6.23959e17i		−	1.90644i
$496$		−	1.89679e16i		−	0.0571991i
$497$	1.96000e17			0.583363
$498$	−2.85292e16			−0.0838106
$499$	1.05367e17			0.305527			0.152763	−	0.988263i	$-0.451183\pi$
$499$	1.05367e17			0.305527			0.152763	+	0.988263i	$0.451183\pi$
$500$	−2.90604e16			−0.0831757
$501$			1.68438e15i			0.00475878i
$502$	−3.81757e17			−1.06467
$503$			4.56753e17i			1.25745i	0.777629	+	0.628724i	$0.216422\pi$
$503$			4.56753e17i			1.25745i	−0.777629	+	0.628724i	$0.783578\pi$
$504$			4.79739e17i			1.30379i
$505$		−	1.31913e17i		−	0.353910i
$506$	−5.08928e17			−1.34796
$507$		−	1.31836e17i		−	0.344732i
$508$			9.40141e16i			0.242705i
$509$	−5.10141e17			−1.30024			−0.650121	−	0.759830i	$-0.725282\pi$
$509$	−5.10141e17			−1.30024			−0.650121	+	0.759830i	$0.725282\pi$
$510$			2.05287e17i			0.516601i
$511$			4.40609e17i			1.09476i
$512$		−	7.14897e16i		−	0.175384i
$513$	4.04909e17			0.980832
$514$			4.55015e16i			0.108834i
$515$	−6.02538e17			−1.42311
$516$	6.33253e16			0.147691
$517$	1.26993e17			0.292476
$518$	3.09072e17			0.702937
$519$			3.19520e17i			0.717645i
$520$			1.94327e17i			0.431035i
$521$	−4.02460e17			−0.881612			−0.440806	−	0.897602i	$-0.645307\pi$
$521$	−4.02460e17			−0.881612			−0.440806	+	0.897602i	$0.645307\pi$
$522$	−2.28051e17	+	3.54579e16i	−0.493371	+	0.0767104i
$523$	4.09991e16			0.0876018			0.0438009	−	0.999040i	$-0.486053\pi$
$523$	4.09991e16			0.0876018			0.0438009	+	0.999040i	$0.486053\pi$
$524$			4.73581e17i			0.999403i
$525$		−	2.64070e17i		−	0.550406i
$526$	−4.39077e17			−0.903928
$527$	5.30656e17			1.07906
$528$	2.72792e16			0.0547913
$529$	5.13268e17			1.01832
$530$			2.50252e17i			0.490439i
$531$	8.07368e17			1.56299
$532$			7.45525e17i			1.42573i
$533$		−	8.64745e16i		−	0.163366i
$534$			7.69785e16i			0.143665i
$535$	4.40324e17			0.811844
$536$		−	4.50333e17i		−	0.820281i
$537$		−	1.48175e17i		−	0.266650i
$538$	−2.89859e17			−0.515349
$539$		−	1.36833e18i		−	2.40360i
$540$			3.72221e17i			0.646014i
$541$		−	1.60644e17i		−	0.275475i	−0.990469	−	0.137737i	$-0.956017\pi$
$541$		−	1.60644e17i		−	0.275475i	0.990469	−	0.137737i	$-0.0439830\pi$
$542$	4.50319e17			0.763000
$543$			5.41264e16i			0.0906171i
$544$	1.02589e18			1.69710
$545$	−4.64960e17			−0.760043
$546$	7.06539e16			0.114126
$547$	−8.38968e17			−1.33915			−0.669573	−	0.742747i	$-0.733523\pi$
$547$	−8.38968e17			−1.33915			−0.669573	+	0.742747i	$0.733523\pi$
$548$			2.71261e17i			0.427872i
$549$			1.09511e17i			0.170701i
$550$	−5.59472e17			−0.861829
$551$	−8.94041e17	+	1.39007e17i	−1.36104	+	0.211618i
$552$	3.52388e17			0.530172
$553$			1.50945e17i			0.224442i
$554$			3.14257e17i			0.461818i
$555$	2.78340e17			0.404270
$556$	−5.32091e16			−0.0763835
$557$	8.46461e17			1.20101			0.600507	−	0.799619i	$-0.294965\pi$
$557$	8.46461e17			1.20101			0.600507	+	0.799619i	$0.294965\pi$
$558$	−2.31404e17			−0.324525
$559$			1.35648e17i			0.188035i
$560$	−1.39845e17			−0.191612
$561$			7.63178e17i			1.03363i
$562$			2.98312e17i			0.399379i
$563$		−	1.29849e18i		−	1.71843i	−0.511613	−	0.859216i	$-0.670952\pi$
$563$		−	1.29849e18i		−	1.71843i	0.511613	−	0.859216i	$-0.329048\pi$
$564$	−3.48558e16			−0.0455996
$565$			1.59719e18i			2.06557i
$566$			1.45072e16i			0.0185471i
$567$	−7.21325e17			−0.911678
$568$			2.87528e17i			0.359266i
$569$			1.05424e18i			1.30229i	0.758952	+	0.651147i	$0.225712\pi$
$569$			1.05424e18i			1.30229i	−0.758952	+	0.651147i	$0.774288\pi$
$570$		−	3.50949e17i		−	0.428605i
$571$	−4.92727e17			−0.594938			−0.297469	−	0.954732i	$-0.596142\pi$
$571$	−4.92727e17			−0.594938			−0.297469	+	0.954732i	$0.596142\pi$
$572$			2.86371e17i			0.341866i
$573$	−3.13456e17			−0.369975
$574$	−4.02156e17			−0.469318
$575$	1.11834e18			1.29042
$576$	−3.81627e17			−0.435405
$577$		−	3.27651e17i		−	0.369631i	−0.982773	−	0.184815i	$-0.940831\pi$
$577$		−	3.27651e17i		−	0.369631i	0.982773	−	0.184815i	$-0.0591687\pi$
$578$			9.22433e17i			1.02897i
$579$	3.89571e15			0.00429710
$580$	−1.27786e17	−	8.21866e17i	−0.139380	−	0.896436i
$581$	5.43710e17			0.586438
$582$			8.54032e16i			0.0910908i
$583$			9.30340e17i			0.981287i
$584$	−6.46364e17			−0.674208
$585$	−3.66851e17			−0.378422
$586$	−4.79305e16			−0.0488965
$587$	1.74203e18			1.75755			0.878773	−	0.477240i	$-0.158363\pi$
$587$	1.74203e18			1.75755			0.878773	+	0.477240i	$0.158363\pi$
$588$			3.75566e17i			0.374743i
$589$	−9.07185e17			−0.895254
$590$		−	1.52092e18i		−	1.48446i
$591$		−	6.10698e17i		−	0.589533i
$592$		−	7.01600e16i		−	0.0669883i
$593$	−4.64820e17			−0.438964			−0.219482	−	0.975617i	$-0.570437\pi$
$593$	−4.64820e17			−0.438964			−0.219482	+	0.975617i	$0.570437\pi$
$594$		−	7.23321e17i		−	0.675646i
$595$		−	3.91236e18i		−	3.61476i
$596$	1.26200e18			1.15334
$597$			1.25320e17i			0.113289i
$598$			2.99220e17i			0.267567i
$599$		−	5.65407e17i		−	0.500134i	−0.968228	−	0.250067i	$-0.919547\pi$
$599$		−	5.65407e17i		−	0.500134i	0.968228	−	0.250067i	$-0.0804527\pi$
$600$	3.87385e17			0.338969
$601$		−	2.55699e17i		−	0.221332i	−0.993858	−	0.110666i	$-0.964702\pi$
$601$		−	2.55699e17i		−	0.221332i	0.993858	−	0.110666i	$-0.0352984\pi$
$602$	6.30842e17			0.540186
$603$	8.50138e17			0.720157
$604$	−1.08000e18			−0.905073
$605$	−2.70351e18			−2.24139
$606$		−	7.03578e16i		−	0.0577086i
$607$		−	2.02919e18i		−	1.64663i	−0.567587	−	0.823313i	$-0.692123\pi$
$607$		−	2.02919e18i		−	1.64663i	0.567587	−	0.823313i	$-0.307877\pi$
$608$	−1.75381e18			−1.40802
$609$	−7.53826e17	+	1.17207e17i	−0.598768	+	0.0930978i
$610$	2.06296e17			0.162124
$611$		−	7.46642e16i		−	0.0580557i
$612$			1.20770e18i			0.929128i
$613$	2.43383e18			1.85267			0.926333	−	0.376705i	$-0.122943\pi$
$613$	2.43383e18			1.85267			0.926333	+	0.376705i	$0.122943\pi$
$614$	1.13400e18			0.854117
$615$	−3.62168e17			−0.269912
$616$	3.35973e18			2.47759
$617$			1.26572e18i			0.923597i	0.886985	+	0.461799i	$0.152796\pi$
$617$			1.26572e18i			0.923597i	−0.886985	+	0.461799i	$0.847204\pi$
$618$	−3.21373e17			−0.232052
$619$		−	2.23526e17i		−	0.159712i	−0.996806	−	0.0798562i	$-0.974554\pi$
$619$		−	2.23526e17i		−	0.159712i	0.996806	−	0.0798562i	$-0.0254461\pi$
$620$		−	8.33948e17i		−	0.589648i
$621$			1.44586e18i			1.01165i
$622$	−2.86653e17			−0.198481
$623$		−	1.46706e18i		−	1.00525i
$624$		−	1.60386e16i		−	0.0108759i
$625$	−1.61421e18			−1.08328
$626$		−	1.68360e17i		−	0.111817i
$627$		−	1.30469e18i		−	0.857569i
$628$			9.13264e17i			0.594099i
$629$	1.96283e18			1.26373
$630$			1.70607e18i			1.08713i
$631$	−1.14209e18			−0.720293			−0.360146	−	0.932896i	$-0.617273\pi$
$631$	−1.14209e18			−0.720293			−0.360146	+	0.932896i	$0.617273\pi$
$632$	−2.21433e17			−0.138223
$633$	−8.81930e17			−0.544892
$634$	8.15526e17			0.498721
$635$			8.43436e17i			0.510532i
$636$		−	2.55351e17i		−	0.152991i
$637$	−8.04495e17			−0.477109
$638$	2.48320e17	+	1.59710e18i	0.145773	+	0.937555i
$639$	−5.42795e17			−0.315413
$640$		−	1.73606e18i		−	0.998606i
$641$			1.38826e18i			0.790484i	0.918577	+	0.395242i	$0.129339\pi$
$641$			1.38826e18i			0.790484i	−0.918577	+	0.395242i	$0.870661\pi$
$642$	2.34854e17			0.132379
$643$	2.81850e18			1.57270			0.786351	−	0.617780i	$-0.211968\pi$
$643$	2.81850e18			1.57270			0.786351	+	0.617780i	$0.211968\pi$
$644$	−2.66214e18			−1.47052
$645$	5.68115e17			0.310669
$646$		−	2.47487e18i		−	1.33980i
$647$	2.20360e18			1.18102			0.590508	−	0.807032i	$-0.298928\pi$
$647$	2.20360e18			1.18102			0.590508	+	0.807032i	$0.298928\pi$
$648$		−	1.05817e18i		−	0.561459i
$649$		−	5.65419e18i		−	2.97016i
$650$			3.28936e17i			0.171070i
$651$	−7.64908e17			−0.393852
$652$			1.22863e18i			0.626342i
$653$			1.87046e18i			0.944090i	0.881575	+	0.472045i	$0.156484\pi$
$653$			1.87046e18i			0.944090i	−0.881575	+	0.472045i	$0.843516\pi$
$654$	−2.47994e17			−0.123933
$655$			4.24867e18i			2.10225i
$656$			9.12901e16i			0.0447248i
$657$		−	1.22021e18i		−	0.591913i
$658$	−3.47231e17			−0.166782
$659$		−	8.59567e17i		−	0.408813i	−0.978886	−	0.204406i	$-0.934474\pi$
$659$		−	8.59567e17i		−	0.408813i	0.978886	−	0.204406i	$-0.0655264\pi$
$660$	1.19937e18			0.564827
$661$	−1.08497e18			−0.505949			−0.252975	−	0.967473i	$-0.581409\pi$
$661$	−1.08497e18			−0.505949			−0.252975	+	0.967473i	$0.581409\pi$
$662$	−1.24021e18			−0.572689
$663$	4.48703e17			0.205173
$664$			7.97612e17i			0.361159i
$665$			6.68839e18i			2.99903i
$666$	−8.55934e17			−0.380065
$667$	−4.96370e17	−	3.19246e18i	−0.218267	−	1.40381i
$668$	1.86670e16			0.00812882
$669$			4.67349e17i			0.201545i
$670$		−	1.60149e18i		−	0.683972i
$671$	7.66929e17			0.324384
$672$	−1.47876e18			−0.619436
$673$	1.36859e18			0.567772			0.283886	−	0.958858i	$-0.408376\pi$
$673$	1.36859e18			0.567772			0.283886	+	0.958858i	$0.408376\pi$
$674$	−1.47771e18			−0.607157
$675$			1.58945e18i			0.646804i
$676$	−1.46106e18			−0.588862
$677$			2.58703e18i			1.03270i	0.856378	+	0.516350i	$0.172710\pi$
$677$			2.58703e18i			1.03270i	−0.856378	+	0.516350i	$0.827290\pi$
$678$			8.51885e17i			0.336812i
$679$		−	1.62761e18i		−	0.637379i
$680$	5.73936e18			2.22616
$681$		−	1.47278e18i		−	0.565826i
$682$			1.62057e18i			0.616695i
$683$	−2.50720e18			−0.945047			−0.472524	−	0.881318i	$-0.656657\pi$
$683$	−2.50720e18			−0.945047			−0.472524	+	0.881318i	$0.656657\pi$
$684$		−	2.06463e18i		−	0.770864i
$685$			2.43358e18i			0.900032i
$686$			1.22063e18i			0.447174i
$687$	−1.75562e18			−0.637107
$688$		−	1.43202e17i		−	0.0514785i
$689$	5.46985e17			0.194783
$690$	1.25318e18			0.442072
$691$	−6.51572e17			−0.227696			−0.113848	−	0.993498i	$-0.536318\pi$
$691$	−6.51572e17			−0.227696			−0.113848	+	0.993498i	$0.536318\pi$
$692$	3.54104e18			1.22586
$693$			6.34249e18i			2.17517i
$694$		−	1.33847e18i		−	0.454751i
$695$	−4.77359e17			−0.160673
$696$	−1.71940e17	−	1.10585e18i	−0.0573345	−	0.368753i
$697$	−2.55398e18			−0.843732
$698$		−	2.25429e18i		−	0.737820i
$699$		−	5.79787e17i		−	0.188004i
$700$	−2.92652e18			−0.940188
$701$	−1.28659e18			−0.409518			−0.204759	−	0.978812i	$-0.565641\pi$
$701$	−1.28659e18			−0.409518			−0.204759	+	0.978812i	$0.565641\pi$
$702$	−4.25270e17			−0.134114
$703$	−3.35557e18			−1.04847
$704$			2.67262e18i			0.827400i
$705$	−3.12705e17			−0.0959191
$706$		−	1.04312e17i		−	0.0317032i
$707$			1.34088e18i			0.403798i
$708$			1.55191e18i			0.463074i
$709$	1.62012e18			0.479011			0.239506	−	0.970895i	$-0.423015\pi$
$709$	1.62012e18			0.479011			0.239506	+	0.970895i	$0.423015\pi$
$710$			1.02252e18i			0.299565i
$711$		−	4.18021e17i		−	0.121352i
$712$	2.15214e18			0.619086
$713$		−	3.23939e18i		−	0.923382i
$714$		−	2.08672e18i		−	0.589423i
$715$			2.56915e18i			0.719117i
$716$	−1.64213e18			−0.455484
$717$			1.98495e18i			0.545600i
$718$	−1.46529e18			−0.399131
$719$	−5.55138e17			−0.149852			−0.0749262	−	0.997189i	$-0.523872\pi$
$719$	−5.55138e17			−0.149852			−0.0749262	+	0.997189i	$0.523872\pi$
$720$	3.87280e17			0.103601
$721$	6.12474e18			1.62371
$722$			2.00086e18i			0.525683i
$723$			1.73387e18i			0.451458i
$724$	5.99849e17			0.154790
$725$	−5.45667e17	−	3.50952e18i	−0.139550	−	0.897533i
$726$	−1.44196e18			−0.365481
$727$			1.04190e18i			0.261728i	0.991400	+	0.130864i	$0.0417751\pi$
$727$			1.04190e18i			0.261728i	−0.991400	+	0.130864i	$0.958225\pi$
$728$		−	1.97532e18i		−	0.491794i
$729$	8.88147e17			0.219157
$730$	−2.29863e18			−0.562173
$731$	4.00631e18			0.971138
$732$	−2.10500e17			−0.0505743
$733$		−	3.40745e18i		−	0.811434i	−0.913999	−	0.405717i	$-0.867022\pi$
$733$		−	3.40745e18i		−	0.811434i	0.913999	−	0.405717i	$-0.132978\pi$
$734$	−1.69129e18			−0.399203
$735$			3.36934e18i			0.788275i
$736$		−	6.26254e18i		−	1.45226i
$737$		−	5.95372e18i		−	1.36852i
$738$	1.11371e18			0.253751
$739$			1.14091e18i			0.257670i	0.991666	+	0.128835i	$0.0411237\pi$
$739$			1.14091e18i			0.257670i	−0.991666	+	0.128835i	$0.958876\pi$
$740$		−	3.08467e18i		−	0.690563i
$741$	−7.67081e17			−0.170225
$742$		−	2.54379e18i		−	0.559572i
$743$			5.12066e18i			1.11660i	0.829638	+	0.558302i	$0.188547\pi$
$743$			5.12066e18i			1.11660i	−0.829638	+	0.558302i	$0.811453\pi$
$744$		−	1.12210e18i		−	0.242555i
$745$	1.13219e19			2.42606
$746$		−	3.10863e18i		−	0.660339i
$747$	−1.50573e18			−0.317076
$748$	8.45783e18			1.76563
$749$	−4.47585e18			−0.926284
$750$	−1.39055e17			−0.0285291
$751$		−	6.06085e18i		−	1.23275i	−0.787454	−	0.616373i	$-0.788601\pi$
$751$		−	6.06085e18i		−	1.23275i	0.787454	−	0.616373i	$-0.211399\pi$
$752$			7.88222e16i			0.0158940i
$753$	3.49467e18			0.698617
$754$	9.38998e17	−	1.45997e17i	0.186102	−	0.0289355i
$755$	−9.68909e18			−1.90383
$756$		−	3.78359e18i		−	0.737077i
$757$		−	8.03326e17i		−	0.155156i	−0.996986	−	0.0775780i	$-0.975281\pi$
$757$		−	8.03326e17i		−	0.155156i	0.996986	−	0.0775780i	$-0.0247187\pi$
$758$	−3.10792e18			−0.595140
$759$	4.65882e18			0.884513
$760$	−9.81173e18			−1.84696
$761$	−5.17894e18			−0.966586			−0.483293	−	0.875459i	$-0.660559\pi$
$761$	−5.17894e18			−0.966586			−0.483293	+	0.875459i	$0.660559\pi$
$762$			4.49861e17i			0.0832474i
$763$	4.72627e18			0.867180
$764$			3.47384e18i			0.631980i
$765$			1.08348e19i			1.95443i
$766$		−	8.21309e17i		−	0.146899i
$767$	−3.32433e18			−0.589568
$768$		−	2.04295e18i		−	0.359262i
$769$		−	1.80458e18i		−	0.314670i	−0.987545	−	0.157335i	$-0.949710\pi$
$769$		−	1.80458e18i		−	0.314670i	0.987545	−	0.157335i	$-0.0502902\pi$
$770$	1.19480e19			2.06588
$771$		−	4.16528e17i		−	0.0714153i
$772$		−	4.31737e16i		−	0.00734019i
$773$		−	2.14969e18i		−	0.362417i	−0.983445	−	0.181209i	$-0.941999\pi$
$773$		−	2.14969e18i		−	0.362417i	0.983445	−	0.181209i	$-0.0580009\pi$
$774$	−1.74703e18			−0.292068
$775$		−	3.56111e18i		−	0.590370i
$776$	2.38768e18			0.392532
$777$	−2.82930e18			−0.461257
$778$	−4.79443e18			−0.775122
$779$	4.36616e18			0.700013
$780$		−	7.05156e17i		−	0.112117i
$781$			3.80132e18i			0.599381i
$782$	8.83729e18			1.38190
$783$	4.53732e18	−	7.05473e17i	0.703637	−	0.109403i
$784$	8.49296e17			0.130619
$785$			8.19324e18i			1.24969i
$786$			2.26610e18i			0.342793i
$787$	−4.55795e17			−0.0683808			−0.0341904	−	0.999415i	$-0.510885\pi$
$787$	−4.55795e17			−0.0683808			−0.0341904	+	0.999415i	$0.510885\pi$
$788$	−6.76800e18			−1.00702
$789$	4.01939e18			0.593143
$790$	−7.87468e17			−0.115254
$791$		−	1.62352e19i		−	2.35674i
$792$	−9.30430e18			−1.33958
$793$		−	4.50909e17i		−	0.0643892i
$794$		−	2.12890e17i		−	0.0301524i
$795$		−	2.29085e18i		−	0.321818i
$796$	1.38884e18			0.193517
$797$		−	6.55370e18i		−	0.905748i	−0.891575	−	0.452874i	$-0.850399\pi$
$797$		−	6.55370e18i		−	0.905748i	0.891575	−	0.452874i	$-0.149601\pi$
$798$			3.56736e18i			0.489022i
$799$	−2.20517e18			−0.299839
$800$		−	6.88451e18i		−	0.928513i
$801$			4.06281e18i			0.543520i
$802$		−	6.72070e18i		−	0.891828i
$803$	−8.54539e18			−1.12481
$804$			1.63412e18i			0.213364i
$805$	−2.38830e19			−3.09326
$806$	9.52802e17			0.122412
$807$	2.65342e18			0.338164
$808$	−1.96704e18			−0.248680
$809$			4.46328e18i			0.559743i	0.960037	+	0.279872i	$0.0902919\pi$
$809$			4.46328e18i			0.559743i	−0.960037	+	0.279872i	$0.909708\pi$
$810$		−	3.76311e18i		−	0.468159i
$811$	1.07848e19			1.33099			0.665497	−	0.746400i	$-0.268220\pi$
$811$	1.07848e19			1.33099			0.665497	+	0.746400i	$0.268220\pi$
$812$	1.29893e18	+	8.35419e18i	0.159027	+	1.02280i
$813$	−4.12230e18			−0.500669
$814$			5.99431e18i			0.722238i
$815$			1.10225e19i			1.31752i
$816$	−4.73691e17			−0.0561706
$817$	−6.84899e18			−0.805718
$818$	7.88190e18			0.919887
$819$	3.72901e18			0.431766
$820$			4.01368e18i			0.461055i
$821$	9.31385e18			1.06145			0.530724	−	0.847545i	$-0.321920\pi$
$821$	9.31385e18			1.06145			0.530724	+	0.847545i	$0.321920\pi$
$822$			1.29799e18i			0.146759i
$823$		−	9.13136e18i		−	1.02432i	−0.858889	−	0.512161i	$-0.828845\pi$
$823$		−	9.13136e18i		−	1.02432i	0.858889	−	0.512161i	$-0.171155\pi$
$824$			8.98487e18i			0.999965i
$825$	5.12150e18			0.565519
$826$			1.54600e19i			1.69371i
$827$		−	8.09591e18i		−	0.879994i	−0.897999	−	0.439997i	$-0.854979\pi$
$827$		−	8.09591e18i		−	0.879994i	0.897999	−	0.439997i	$-0.145021\pi$
$828$	7.37242e18			0.795084
$829$			7.29411e18i			0.780491i	0.920711	+	0.390245i	$0.127610\pi$
$829$			7.29411e18i			0.780491i	−0.920711	+	0.390245i	$0.872390\pi$
$830$			2.83650e18i			0.301144i
$831$		−	2.87676e18i		−	0.303038i
$832$	1.57135e18			0.164237
$833$			2.37604e19i			2.46411i
$834$	−2.54607e17			−0.0261994
$835$	1.67469e17			0.0170990
$836$	−1.44591e19			−1.46487
$837$	4.60403e18			0.462831
$838$		−	1.15304e18i		−	0.115016i
$839$		−	1.32795e19i		−	1.31440i	−0.753716	−	0.657201i	$-0.771740\pi$
$839$		−	1.32795e19i		−	1.31440i	0.753716	−	0.657201i	$-0.228260\pi$
$840$	−8.27293e18			−0.812539
$841$	−9.77624e18	+	3.11538e18i	−0.952792	+	0.303624i
$842$	−7.67592e17			−0.0742338
$843$		−	2.73080e18i		−	0.262066i
$844$			9.77389e18i			0.930769i
$845$	−1.31077e19			−1.23868
$846$	9.61609e17			0.0901761
$847$	2.74809e19			2.55734
$848$	−5.77445e17			−0.0533258
$849$		−	1.32801e17i		−	0.0121703i
$850$	9.71497e18			0.883524
$851$		−	1.19821e19i		−	1.08141i
$852$		−	1.04335e18i		−	0.0934487i
$853$			1.75466e19i			1.55964i	0.626002	+	0.779822i	$0.284690\pi$
$853$			1.75466e19i			1.55964i	−0.626002	+	0.779822i	$0.715310\pi$
$854$	−2.09698e18			−0.184977
$855$		−	1.85226e19i		−	1.62152i
$856$		−	6.56599e18i		−	0.570454i
$857$	5.74247e18			0.495135			0.247567	−	0.968871i	$-0.420369\pi$
$857$	5.74247e18			0.495135			0.247567	+	0.968871i	$0.420369\pi$
$858$			1.37030e18i			0.117259i
$859$			1.35553e19i			1.15121i	0.817729	+	0.575603i	$0.195233\pi$
$859$			1.35553e19i			1.15121i	−0.817729	+	0.575603i	$0.804767\pi$
$860$		−	6.29607e18i		−	0.530677i
$861$	3.68140e18			0.307959
$862$		−	5.21800e18i		−	0.433218i
$863$	−2.17629e19			−1.79327			−0.896636	−	0.442769i	$-0.853996\pi$
$863$	−2.17629e19			−1.79327			−0.896636	+	0.442769i	$0.853996\pi$
$864$	8.90072e18			0.727924
$865$	3.17680e19			2.57861
$866$	4.26389e18			0.343510
$867$		−	8.44411e18i		−	0.675196i
$868$			8.47701e18i			0.672767i
$869$	−2.92750e18			−0.230605
$870$	−6.11458e17	−	3.93266e18i	−0.0478070	−	0.307476i
$871$	−3.50044e18			−0.271647
$872$			6.93335e18i			0.534055i
$873$			4.50746e18i			0.344619i
$874$	−1.51078e19			−1.14651
$875$	2.65011e18			0.199623
$876$	2.34546e18			0.175368
$877$	−5.65633e18			−0.419795			−0.209897	−	0.977723i	$-0.567313\pi$
$877$	−5.65633e18			−0.419795			−0.209897	+	0.977723i	$0.567313\pi$
$878$			1.38920e19i			1.02341i
$879$	4.38764e17			0.0320851
$880$		−	2.71222e18i		−	0.196873i
$881$			7.75459e18i			0.558747i	0.960183	+	0.279373i	$0.0901268\pi$
$881$			7.75459e18i			0.558747i	−0.960183	+	0.279373i	$0.909873\pi$
$882$		−	1.03612e19i		−	0.741078i
$883$	−2.60307e19			−1.84816			−0.924082	−	0.382194i	$-0.875168\pi$
$883$	−2.60307e19			−1.84816			−0.924082	+	0.382194i	$0.875168\pi$
$884$		−	4.97270e18i		−	0.350472i
$885$			1.39228e19i			0.974080i
$886$	2.33710e18			0.162315
$887$		−	5.57573e18i		−	0.384413i	−0.981354	−	0.192207i	$-0.938436\pi$
$887$		−	5.57573e18i		−	0.384413i	0.981354	−	0.192207i	$-0.0615644\pi$
$888$		−	4.15053e18i		−	0.284066i
$889$		−	8.57345e18i		−	0.582498i
$890$	7.65354e18			0.516211
$891$		−	1.39898e19i		−	0.936710i
$892$	5.17935e18			0.344273
$893$	3.76985e18			0.248765
$894$	6.03870e18			0.395594
$895$	−1.47322e19			−0.958114
$896$			1.76469e19i			1.13937i
$897$		−	2.73911e18i		−	0.175573i
$898$	−1.18567e19			−0.754517
$899$	−1.01657e19	+	1.58059e18i	−0.642244	+	0.0998574i
$900$	8.10461e18			0.508342
$901$		−	1.61549e19i		−	1.00599i
$902$		−	7.79961e18i		−	0.482204i
$903$	−5.77484e18			−0.354462
$904$	2.38168e19			1.45140
$905$	5.38148e18			0.325601
$906$	−5.16784e18			−0.310438
$907$			1.65642e19i			0.987922i	0.869484	+	0.493961i	$0.164451\pi$
$907$			1.65642e19i			0.987922i	−0.869484	+	0.493961i	$0.835549\pi$
$908$	−1.63220e19			−0.966528
$909$		−	3.71338e18i		−	0.218326i
$910$		−	7.02471e18i		−	0.410071i
$911$		−	2.26276e19i		−	1.31150i	−0.754978	−	0.655750i	$-0.772352\pi$
$911$		−	2.26276e19i		−	1.31150i	0.754978	−	0.655750i	$-0.227648\pi$
$912$	8.09799e17			0.0466027
$913$			1.05450e19i			0.602540i
$914$		−	1.97343e18i		−	0.111962i
$915$	−1.88847e18			−0.106383
$916$			1.94565e19i			1.08829i
$917$		−	4.31874e19i		−	2.39859i
$918$			1.25601e19i			0.692654i
$919$	1.51666e19			0.830494			0.415247	−	0.909709i	$-0.363695\pi$
$919$	1.51666e19			0.830494			0.415247	+	0.909709i	$0.363695\pi$
$920$		−	3.50359e19i		−	1.90499i
$921$	−1.03808e19			−0.560458
$922$	1.32566e19			0.710694
$923$	2.23495e18			0.118975
$924$	−1.21914e19			−0.644447
$925$		−	1.31721e19i		−	0.691408i
$926$		−	1.57467e19i		−	0.820762i
$927$	−1.69616e19			−0.877908
$928$	−1.96528e19	+	3.05567e18i	−1.01010	+	0.157052i
$929$	−1.83546e19			−0.936793			−0.468397	−	0.883518i	$-0.655168\pi$
$929$	−1.83546e19			−0.936793			−0.468397	+	0.883518i	$0.655168\pi$
$930$		−	3.99047e18i		−	0.202248i
$931$		−	4.06196e19i		−	2.04438i
$932$	−6.42542e18			−0.321143
$933$	2.62407e18			0.130240
$934$	1.39657e19			0.688348
$935$	7.58784e19			3.71401
$936$			5.47038e18i			0.265904i
$937$	−1.19734e19			−0.577977			−0.288988	−	0.957333i	$-0.593319\pi$
$937$	−1.19734e19			−0.577977			−0.288988	+	0.957333i	$0.593319\pi$
$938$			1.62790e19i			0.780387i
$939$			1.54120e18i			0.0733723i
$940$			3.46552e18i			0.163846i
$941$	1.06597e19			0.500511			0.250255	−	0.968180i	$-0.419485\pi$
$941$	1.06597e19			0.500511			0.250255	+	0.968180i	$0.419485\pi$
$942$			4.37000e18i			0.203775i
$943$			1.55908e19i			0.722007i
$944$	3.50946e18			0.161407
$945$		−	3.39441e19i		−	1.55045i
$946$			1.22349e19i			0.555018i
$947$			4.30530e19i			1.93967i	0.243754	+	0.969837i	$0.421621\pi$
$947$			4.30530e19i			1.93967i	−0.243754	+	0.969837i	$0.578379\pi$
$948$	8.03513e17			0.0359533
$949$			5.02418e18i			0.223272i
$950$	−1.66082e19			−0.733027
$951$	−7.46547e18			−0.327253
$952$	−5.83401e19			−2.53996
$953$	3.01117e19			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$953$	3.01117e19			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$954$			7.04468e18i			0.302550i
$955$			3.11652e19i			1.32938i
$956$	2.19980e19			0.931979
$957$	−2.27316e18	−	1.46201e19i	−0.0956540	−	0.615209i
$958$	1.62066e19			0.677355
$959$		−	2.47372e19i		−	1.02690i
$960$		−	6.58102e18i		−	0.271350i
$961$	1.41024e19			0.577551
$962$	3.52430e18			0.143362
$963$	1.23953e19			0.500824
$964$	1.92154e19			0.771167
$965$		−	3.87328e17i		−	0.0154401i
$966$	−1.27384e19			−0.504387
$967$		−	1.22416e19i		−	0.481466i	−0.970591	−	0.240733i	$-0.922612\pi$
$967$		−	1.22416e19i		−	0.481466i	0.970591	−	0.240733i	$-0.0773878\pi$
$968$			4.03139e19i			1.57494i
$969$			2.26553e19i			0.879157i
$970$	8.49115e18			0.327303
$971$			3.93700e19i			1.50744i	0.657196	+	0.753720i	$0.271743\pi$
$971$			3.93700e19i			1.50744i	−0.657196	+	0.753720i	$0.728257\pi$
$972$			1.61353e19i			0.613686i
$973$	4.85231e18			0.183322
$974$		−	8.51006e17i		−	0.0319374i
$975$		−	3.01114e18i		−	0.112254i
$976$			4.76019e17i			0.0176279i
$977$	−1.36112e19			−0.500703			−0.250352	−	0.968155i	$-0.580546\pi$
$977$	−1.36112e19			−0.500703			−0.250352	+	0.968155i	$0.580546\pi$
$978$			5.87903e18i			0.214834i
$979$	2.84529e19			1.03285
$980$	3.73404e19			1.34651
$981$	−1.30888e19			−0.468868
$982$	−1.67851e19			−0.597309
$983$			1.50410e18i			0.0531714i	0.999647	+	0.0265857i	$0.00846349\pi$
$983$			1.50410e18i			0.0531714i	−0.999647	+	0.0265857i	$0.991537\pi$
$984$			5.40054e18i			0.189657i
$985$	−6.07183e19			−2.11828
$986$	−4.31196e18	−	2.77328e19i	−0.149443	−	0.961156i
$987$	3.17861e18			0.109440
$988$			8.50109e18i			0.290773i
$989$		−	2.44565e19i		−	0.831033i
$990$	−3.30883e19			−1.11698
$991$	−3.14934e19			−1.05619			−0.528093	−	0.849187i	$-0.677093\pi$
$991$	−3.14934e19			−1.05619			−0.528093	+	0.849187i	$0.677093\pi$
$992$	−1.99418e19			−0.664412
$993$	1.13531e19			0.375790
$994$		−	1.03938e19i		−	0.341793i
$995$	1.24599e19			0.407064
$996$		−	2.89429e18i		−	0.0939413i
$997$		−	4.81770e19i		−	1.55354i	−0.629786	−	0.776769i	$-0.716858\pi$
$997$		−	4.81770e19i		−	1.55354i	0.629786	−	0.776769i	$-0.283142\pi$
$998$		−	5.58755e18i		−	0.179008i
$999$	1.70297e19			0.542041

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.14.b.a.28.12	✓	32
29.28	even	2	inner	29.14.b.a.28.21	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.14.b.a.28.12	✓	32	1.1	even	1	trivial
29.14.b.a.28.21	yes	32	29.28	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	29.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-53.0296i q^{2} +485.442i q^{3} +5379.86 q^{4} +48264.8 q^{5} +25742.8 q^{6} -490607. q^{7} -719711. i q^{8} +1.35867e6 q^{9} +O(q^{10})\)	\(q-53.0296i q^{2} +485.442i q^{3} +5379.86 q^{4} +48264.8 q^{5} +25742.8 q^{6} -490607. q^{7} -719711. i q^{8} +1.35867e6 q^{9} -2.55946e6i q^{10} -9.51508e6i q^{11} +2.61161e6i q^{12} -5.59430e6 q^{13} +2.60167e7i q^{14} +2.34298e7i q^{15} +5.90584e6 q^{16} +1.65225e8i q^{17} -7.20497e7i q^{18} -2.82460e8i q^{19} +2.59658e8 q^{20} -2.38161e8i q^{21} -5.04581e8 q^{22} +1.00862e9 q^{23} +3.49378e8 q^{24} +1.10879e9 q^{25} +2.96664e8i q^{26} +1.43351e9i q^{27} -2.63940e9 q^{28} +(-4.92131e8 - 3.16519e9i) q^{29} +1.24247e9 q^{30} -3.21172e9i q^{31} -6.20905e9i q^{32} +4.61902e9 q^{33} +8.76181e9 q^{34} -2.36790e10 q^{35} +7.30945e9 q^{36} -1.18798e10i q^{37} -1.49788e10 q^{38} -2.71571e9i q^{39} -3.47367e10i q^{40} +1.54576e10i q^{41} -1.26296e10 q^{42} -2.42476e10i q^{43} -5.11898e10i q^{44} +6.55758e10 q^{45} -5.34865e10i q^{46} +1.33465e10i q^{47} +2.86695e9i q^{48} +1.43806e11 q^{49} -5.87984e10i q^{50} -8.02071e10 q^{51} -3.00966e10 q^{52} -9.77753e10 q^{53} +7.60183e10 q^{54} -4.59243e11i q^{55} +3.53095e11i q^{56} +1.37118e11 q^{57} +(-1.67849e11 + 2.60975e10i) q^{58} +5.94235e11 q^{59} +1.26049e11i q^{60} +8.06015e10i q^{61} -1.70316e11 q^{62} -6.66572e11 q^{63} -2.80883e11 q^{64} -2.70008e11 q^{65} -2.44945e11i q^{66} +6.25714e11 q^{67} +8.88887e11i q^{68} +4.89624e11i q^{69} +1.25569e12i q^{70} -3.99505e11 q^{71} -9.77848e11i q^{72} -8.98089e11i q^{73} -6.29980e11 q^{74} +5.38251e11i q^{75} -1.51960e12i q^{76} +4.66816e12i q^{77} -1.44013e11 q^{78} -3.07669e11i q^{79} +2.85044e11 q^{80} +1.47027e12 q^{81} +8.19710e11 q^{82} -1.10824e12 q^{83} -1.28127e12i q^{84} +7.97454e12i q^{85} -1.28584e12 q^{86} +(1.53652e12 - 2.38901e11i) q^{87} -6.84810e12 q^{88} +2.99029e12i q^{89} -3.47746e12i q^{90} +2.74460e12 q^{91} +5.42621e12 q^{92} +1.55911e12 q^{93} +7.07758e11 q^{94} -1.36329e13i q^{95} +3.01414e12 q^{96} +3.31755e12i q^{97} -7.62598e12i q^{98} -1.29278e13i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 131436 q^{4} - 90794 q^{5} - 191952 q^{6} + 398260 q^{7} - 18624674 q^{9}+O(q^{10}) \) 32 * q - 131436 * q^4 - 90794 * q^5 - 191952 * q^6 + 398260 * q^7 - 18624674 * q^9	\( 32 q - 131436 q^{4} - 90794 q^{5} - 191952 q^{6} + 398260 q^{7} - 18624674 q^{9} + 5240482 q^{13} + 549733588 q^{16} + 593107012 q^{20} - 1351453384 q^{22} + 1866943772 q^{23} + 4550583596 q^{24} + 7169723618 q^{25} - 13976463456 q^{28} - 10157197956 q^{29} + 21508715952 q^{30} - 8142086534 q^{33} + 21000232616 q^{34} - 15057663628 q^{35} + 116060443480 q^{36} - 86572746688 q^{38} + 13537077480 q^{42} + 263177965664 q^{45} + 513778986120 q^{49} - 372662169044 q^{51} - 101448215388 q^{52} + 573910354530 q^{53} + 1479431015408 q^{54} + 500871600416 q^{57} - 969686686880 q^{58} + 1024205768724 q^{59} + 1751113369840 q^{62} - 4168751771256 q^{63} - 2804312517964 q^{64} - 781490399506 q^{65} - 872679676184 q^{67} - 1363415929136 q^{71} - 6756459308672 q^{74} - 23715100786248 q^{78} + 1267893681036 q^{80} + 25379587936536 q^{81} + 4236061808312 q^{82} + 6421393088172 q^{83} - 16601603597496 q^{86} + 3240260232764 q^{87} + 3526967972716 q^{88} - 5472886962916 q^{91} + 1684734140256 q^{92} + 3555997675886 q^{93} + 29362958775032 q^{94} - 39622013504436 q^{96}+O(q^{100}) \) 32 * q - 131436 * q^4 - 90794 * q^5 - 191952 * q^6 + 398260 * q^7 - 18624674 * q^9 + 5240482 * q^13 + 549733588 * q^16 + 593107012 * q^20 - 1351453384 * q^22 + 1866943772 * q^23 + 4550583596 * q^24 + 7169723618 * q^25 - 13976463456 * q^28 - 10157197956 * q^29 + 21508715952 * q^30 - 8142086534 * q^33 + 21000232616 * q^34 - 15057663628 * q^35 + 116060443480 * q^36 - 86572746688 * q^38 + 13537077480 * q^42 + 263177965664 * q^45 + 513778986120 * q^49 - 372662169044 * q^51 - 101448215388 * q^52 + 573910354530 * q^53 + 1479431015408 * q^54 + 500871600416 * q^57 - 969686686880 * q^58 + 1024205768724 * q^59 + 1751113369840 * q^62 - 4168751771256 * q^63 - 2804312517964 * q^64 - 781490399506 * q^65 - 872679676184 * q^67 - 1363415929136 * q^71 - 6756459308672 * q^74 - 23715100786248 * q^78 + 1267893681036 * q^80 + 25379587936536 * q^81 + 4236061808312 * q^82 + 6421393088172 * q^83 - 16601603597496 * q^86 + 3240260232764 * q^87 + 3526967972716 * q^88 - 5472886962916 * q^91 + 1684734140256 * q^92 + 3555997675886 * q^93 + 29362958775032 * q^94 - 39622013504436 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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